I have been trying to compute the following complicated integral along with summation, details codes/function of which is given below:
A[n_, ν_, m_, l0_, M_, h_, κ_, τ_] := (
2 Sqrt[2])/(l0*l0)*
Sqrt[(ν!*(2*ν + Abs[m] + 1))/(ν + Abs[m])!]*
Sqrt[(n - (Abs[m] + m)/2)!/(n + (Abs[m] - m)/2)!]*
Integrate[
Exp[-I*κ*M/τ*r^2/(2*h)]*Exp[-r^2/l0^2]*((2*r^2)/l0^2)^(
Abs[m]/2)*(r^2/l0^2)^(Abs[m]/2)*Exp[-r^2/(2*l0^2)]*
LaguerreL[ν, Abs[m], ((2*r^2)/l0^2)]*
LaguerreL[(n - (Abs[m] + m)/2), Abs[m], (r^2/l0^2)]*r, {r, 0,
Infinity}]
A[1, 2, -1, 1*10^-9, 1*10^-30, 1*10^-34, 1, 2]
P[n_, l0_, l1_, M_, ω1_,
h_, κ_, τ_, Ω_] :=
NSum[A[n, ν, m, l0, M, h, κ, τ]*(2 Sqrt[2])/(l0*l1)*
Sqrt[(ν!*(2*ν + Abs[m] + 1))/(ν + Abs[m])!]*
Sqrt[(n - (Abs[m] + m)/2)!/(n + (Abs[m] - m)/2)!]*
NIntegrate[
Exp[-r^2/(2*l1^2)]*(r^2/l1^2)^(Abs[m]/2)*
LaguerreL[(n - (Abs[m] + m)/2), Abs[m], (r^2/l1^2)]*
Exp[I*m*Ω*τ]*
Exp[-2*I*(2 ν + Abs[m] + 1)*ω1*τ]*
Exp[-I*κ*M/τ*(l0/l1)*r^2/(2*h)]*
Exp[-r^2/l1^2]*((2*r^2)/l1^2)^(Abs[m]/2)*
LaguerreL[ν, Abs[m], ((2*r^2)/l1^2)]*r, {r, 0,
Infinity}], {ν, 1, 10, 1}, {m, -n, n, 1}]
P[2, 1*10^-9, 2*10^-9, 1*10^-30, 0.25*10^14, 1*10^-34, 1, 2,
0.5*10^14]
P1 = DiscretePlot[(Abs[
P[n, 1*10^-9, 2*10^-9, 1*10^-30, 0.25*10^14, 1*10^-34, 1, 2,
0.5*10^14]])^2, {n, 1, 10}, PlotStyle -> Red, PlotRange -> Full]
Kindly peruse the 2nd input line, which produces a huge division under "Integrate" function but otherwise finite. on the other hand, the same integral under "NIntegrate" function shows "1/0", which in turn suppresses the further output. I have gone through the similar posts under heading "different results under Integrate and NIntegrate", where it has been shown that both the results after some simplification is identical.
Moreover, the 4th inputline does not produce any output, even no error message is shown. As no result comes out in the intermidiate steps, the final plot is not obtained. It appears to me that somehow I can not use the appropriate code or function for such kind of complicated integration /sum.
Would you kindly correct the codes, I have used, or suggest me any relevant posts, which may help me. Thanking you...
A
insideNSum
. $\endgroup$